Question

Triangle A has sides of lengths `32`, `44`, and `64`. Triangle B is similar to triangle A and has a side of length `8`. What are the possible lengths of the other two sides of triangle B?

Answer 1

Possible length of sides of triangle are (8, 11 and 16), (5.82, 8 and 11.64) and (4, 5.5 and 8).

Explanation:

Sides of two similar triangles are proportional to each other.

As triangle A has sides of lengths 32, 44, and 64 and triangle B is similar to triangle A and has a side of length 8, the latter could be proportional to 32, 44 or 64.

If it is proportional to 32, other two sides could be `8*44/32=11` and `8*64/32=16` and three sides would be 8, 11 and 16.

If it is proportional to 44, other two sides could be `8*32/44=5.82` and `8*64/44=11.64` and three side would be 5.82, 8 and 11.64.

If it is proportional to 64, other two sides could be `8*32/64=4` and `8*44/64=5.5` and three sides would be 4, 5.5 and 8.